Analytic Approach in Quantum Chromodynamics

TL;DR

This paper introduces a new analytic formulation in quantum chromodynamics that eliminates unphysical singularities and provides stable, higher-loop consistent calculations for physical processes, with applications to lepton-nucleon scattering.

Contribution

The paper develops a renormalization invariant analytic scheme in QCD that removes ghost poles and ensures stability across higher-loop calculations and different renormalization schemes.

Findings

Unphysical ghost singularities are eliminated by the new scheme.

Calculations are stable with respect to higher-loop effects.

Modified structure function moments have desirable analytic properties.

Abstract

We investigate a new ``renormalization invariant analytic formulation'' of calculations in quantum chromodynamics, where the renormalization group summation is correlated with the analyticity with respect to the square of the transferred momentum $Q^2$. The expressions for the invariant charge and matrix elements are then modified such that the unphysical singularities of the ghost pole type do not appear at all, being by construction compensated by additional nonperturbative contributions. Using the new scheme, we show that the results of calculations for a number of physical processes are stable with respect to higher-loop effects and the choice of the renormalization prescription. Having in mind applications of the new formulation to inelastic lepton-nucleon scattering processes, we analyze the corresponding structure functions starting from the general principles of the theory expressed by the Jost-Lehmann-Dyson integral representation. We use a nonstandard scaling variable that leads to modified moments of the structure functions possessing K\"all\'en-Lehmann analytic properties with respect to $Q^2$. We find the relation between these ``modified analytic moments'' and the operator product expansion.